(Wiley IEEE) juan a martinez velasco transient analysis of power systems solution techniques, tools and applications wiley IEEE press (2015)

TRANSIENT ANALYSIS OF POWER SYSTEMS SOLUTION TECHNIQUES, TOOLS AND APPLICATIONS EDITOR JUAN A... 6.3 Modelling Guidelines 2066.4.1 Simulation of an Independent PFC in a Single Line Appl

TRANSIENT ANALYSIS

OF POWER SYSTEMS SOLUTION TECHNIQUES, TOOLS AND APPLICATIONS

EDITOR

JUAN A MARTINEZ-VELASCO

TRANSIENT ANALYSIS

OF POWER SYSTEMS

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Library of Congress Cataloging-in-Publication Data

1 Introduction to Electromagnetic Transient Analysis of Power Systems 1

Juan A Martinez-Velasco

2 Solution Techniques for Electromagnetic Transients in Power Systems 9

Jean Mahseredjian, Ilhan Kocar and Ulas Karaagac

2.5.1 Nodal Analysis and Modified-Augmented-Nodal-Analysis 13

3.2 Frequency Domain Basics 40

4 Real-Time Simulation Technologies in Engineering 72

Christian Dufour and Jean B´elanger

4.3.6 Effective Parallel Processing for Fast EMT Simulation 77

4.3.8 Advanced Parallel Solvers without Artificial Delays or Stublines:

4.7.2 Monte Carlo Tests for Power Grid Switching Surge System Studies 87

4.8.1 Industrial Motor Drive Design and Testing Using CPU Models 90

4.10.2 Aircraft Flight Parameter Identification 95

Juan A Martinez-Velasco and Francisco Gonz´alez-Molina

6.3 Modelling Guidelines 206

6.4.1 Simulation of an Independent PFC in a Single Line Application 212

7 Applications of Power Electronic Devices in Distribution Systems 248

Arindam Ghosh and Farhad Shahnia

8 Modelling of Electronically Interfaced DER Systems for Transient Analysis 280

Amirnaser Yazdani and Omid Alizadeh

8.5 Examples 288

8.5.2 Example 2: Direct-Drive Variable-Speed Wind Energy System 298

9 Simulation of Transients for VSC-HVDC Transmission Systems Based on

Hani Saad, S´ebastien Denneti`ere, Jean Mahseredjian, Tarek Ould-Bachir and

Jean-Pierre David

10 Dynamic Average Modelling of Rectifier Loads and AC-DC Converters for

Sina Chiniforoosh, Juri Jatskevich, Hamid Atighechi and Juan A Martinez-Velasco

10.5.3 Dynamic Performance Under Balanced and Unbalanced Conditions 377

10.5.4 Input Sequence Impedances under Unbalanced Conditions 382

11.7.2 Case Study 1: Simulation of an Electromechanical Distance Relay 428

11.7.3 Case Study 2: Simulation of a Numerical Distance Relay 430

11.8 Protection of Distribution Systems 450

11.8.2 Protection of Distribution Systems with Distributed Generation 451

11.8.3 Modelling of Distribution Feeder Protective Devices 451

11.8.4 Protection of the Interconnection of Distributed Generators 460

13 Interfacing Methods for Electromagnetic Transient Simulation:

New Possibilities for Analysis and Design 552

13.4 Interfacing Implementation Options: External vs Internal Interfaces 555

13.6.2 Wrapper Interfacing: Run-Controllers and Multiple-Runs 560

Annex A: Techniques and Computer Codes for Rational Modelling of

Frequency-Dependent Components and Subnetworks 568

Bjørn Gustavsen

The story of this book may be traced back to the General Meeting that the IEEE Power and EnergySociety held in July 2010, when the Analysis of System Transients using Digital Programs WorkingGroup gave a tutorial course on ‘Transient analysis of power systems Solution techniques, tools andapplications’ The tutorial provided a basic background to the main aspects to be considered whenperforming electromagnetic transients studies (solution techniques, parameter determination, modellingguidelines), detailed some of the main applications of present transients tools (overvoltage calcula-tion, power electronics applications, protection) and discussed more recent developments (e.g dynamicaverage models and interfacing techniques) mostly aimed at overcoming some of the current limitations.This book was initially thought of as an expanded version of the material used in the tutorial; however,several important fields were not covered in the tutorial, such as smart grid simulation, HVDC analysisdistributed energy resources and custom power modelling Therefore, rather than expanding the tutorialchapters, this book has incorporated new material by adding chapters and providing a broader coverage

of fields related to transient analysis of power systems

Although this is a book on electromagnetic transients, some important topics related to this field arenot well covered or not covered at all For instance, parallel computing will become a very importantaspect in the future development of software tools for simulating transients in power systems; except

in those chapters that deal with real-time simulation, nothing on this field has been included in thisbook Another aspect that will be fundamental to the analysis and design of the future smart grid is thecombined simulation of communication and power systems; the book includes a chapter dedicated toanalysing the possibilities that time-domain simulation offers in the analysis of smart grid technologieswithout considering the representation of the communication system

It is also worth mentioning that the topics covered in most chapters require a previous background onelectromagnetic transient analysis The book is mainly addressed to graduate students and professionalsinvolved in transient studies

As with any other previous book in which I have been involved, I want to finish this Preface thankingmembers of the IEEE WG, friends and relatives for their help and, in many circumstances, for theirpatience

Juan A Martinez-Velasco

Barcelona, Spain March 2014

About the Editor

Juan A Martinez-Velascowas born in Barcelona, Spain He received the Ingeniero Industrial andDoctor Ingeniero Industrial degrees from the Universitat Polit`ecnica de Catalunya (UPC), Spain He iscurrently with the Departament d’Enginyeria El`ectrica of the UPC

He has authored and coauthored more than 200 journal and conference papers, most of them ontransient analysis of power systems He has been involved in several EMTP (ElectroMagnetic TransientsProgram) courses and worked as a consultant for some Spanish companies His teaching and researchareas cover power systems analysis, transmission and distribution, power quality and electromagnetictransients He is an active member of several IEEE and CIGRE Working Groups Presently, he is thechair of the IEEE General Systems Subcommittee

He has been involved as editor or co-author of several books He is also coeditor of the IEEE publication

“Modeling and Analysis of System Transients Using Digital Programs” (1999) In 2010, he was thecoordinator of the tutorial course “Transient Analysis of Power Systems Solution Techniques, Tools,and Applications”, given at the 2010 IEEE PES General Meeting, July 2010, and held in Minneapolis

In 1999, he got the “1999 PES Working Group Award for Technical Report”, for his participation inthe tasks performed by the IEEE Task Force on Modeling and Analysis of Slow Transients In 2000, hegot the “2000 PES Working Group Award for Technical Report”, for his participation in the edition of thespecial publication “Modeling and Analysis of System Transients using Digital Programs” In 2009, hegot the “Technical Committee Working Group Award” of the IEEE PES Transmission and DistributionCommittee

List of Contributors

Omid Alizadeh,Ryerson University, Toronto, ON, Canada

Udaya D Annakkage,University of Manitoba, Winnipeg, MB, Canada

Hamid Atighechi,BC Hydro, Vancouver, BC, Canada

Tarek Ould-Bachir, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Jean B´elanger,OPAL-RT Technologies, Montr´eal, QC, Canada

Sina Chiniforoosh,BC Hydro, Burnaby, BC, Canada

Jean-Pierre David, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Francisco de Le´on,NYU Polytechnic School of Engineering, Brooklyn, NY, USA

S´ebastien Denneti`ere,R´eseau de Transport d’Electricit´e (RTE), Paris, France

Christian Dufour,OPAL-RT Technologies, Montr´eal, QC, Canada

Shaahin Filizadeh,University of Manitoba, Winnipeg, MB, Canada

Arindam Ghosh,Curtin University, Perth, Australia

Francisco Gonz´alez-Molina,Universitat Rovira i Virgili, Tarragona, Spain

Bjørn Gustavsen,SINTEF Energy Research, Trondheim, Norway

Jos´e A Guti´errez-Robles,Universidad de Guadalajara, Guadalajara, Mexico

Juri Jatskevich,University of British Columbia, Vancouver, BC, Canada

Ulas Karaagac, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Ilhan Kocar, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Jean Mahseredjian, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Jos´e L Naredo,CINVESTAV, Guadalajara, Mexico

Xuanchang Ran,NYU Polytechnic School of Engineering, Brooklyn, NY, USA

Hani Saad, ´Ecole Polytechnique de Montr´eal, Montr´eal, QC, Canada

Reynaldo Salcedo,NYU Polytechnic School of Engineering, Brooklyn, NY, USA

Kalyan K Sen,Sen Engineering Solutions, Monroeville, PA, USA

Farhad Shahnia,Curtin University, Perth, Australia

Amirnaser Yazdani,Ryerson University, Toronto, ON, Canada

Power systems play a crucial role in modern society, and their operation is based on some specificprinciples Since electricity cannot be stored in large quantities, the operation of the power system mustachieve a permanent balance between its production in power stations and its consumption by loads inorder to maintain frequency within narrow limits and ensure a reliable service.

Even when the power system is running under normal operation, loads are continually connected anddisconnected, and some control actions are required to maintain voltage and frequency within limits Thismeans that the power system is never operating in a steady state In addition, unscheduled disturbancescan alter the normal operation of the power system, force a change in its configuration, cause failure ofsome power equipment or cause an interruption of service that can affect a significant percentage of thesystem demand, such as a blackout

The analysis and simulation of electromagnetic transients has become a fundamental methodologyfor understanding the performance of power systems, determining power component ratings, explain-ing equipment failures or testing protection devices The study of transients is a mature field thatcan be used in the design of modern power systems Since the first steps in this field, a significanteffort has been dedicated to the development of new techniques and more powerful software tools.Sophisticated models, complex solution techniques and powerful simulation tools have been developed

to perform studies that are of paramount importance in the design of modern power systems Thefirst developments of transients tools were mostly aimed at calculating overvoltages Presently, thesetools are applied in a myriad of studies (e.g FACTS and custom power applications, protective relay

Transient Analysis of Power Systems: Solution Techniques, Tools and Applications, First Edition.

Edited by Juan A Martinez-Velasco.

© 2015 John Wiley & Sons, Ltd Published 2015 by John Wiley & Sons, Ltd.

performance, power quality studies) for which detailed models and accurate solutions can be extremelyimportant.

Transient phenomena in power systems are associated with disturbances caused by faults, switchingoperations, lightning strikes or load variations These phenomena can stress and damage power equip-ment The paramount importance of their study relates to the effects they can have on system performance

or the failures they can cause to power equipment

Two types of stress can be caused by transient phenomena in power systems: (1) overcurrents, whichcan damage power equipment due to excessive heat dissipation, and (2) overvoltages, which can causeinsulation breakdown (failure through solid or liquid insulation) or flashovers (insulation failure throughair) Protection against these stresses is therefore necessary This protection can be provided by specializedequipment whose operation is aimed at either isolating the power system section where the disturbancehas occurred (e.g a power component failure that causes short-circuit) or limiting the stress across powerequipment terminals (e.g by installing a surge arrester that will mitigate voltage stresses) In addition, abetter ability to handle stresses caused by transient phenomena can be also achieved through good design

of power equipment (e.g by shielding overhead transmission lines to limit flashovers caused by directlightning strikes) That is, although the power system operates most of the time under normal operatingconditions, its design must enable it to cope with the consequences of transient phenomena

In order to provide adequate protection against both types of stresses, it is fundamental to knowtheir origin, calculate their main characteristics and estimate the most adverse operating conditions Arigorous and accurate analysis of transients in power systems is difficult due to the size of the system,the complexity of the interaction between power devices and the physical phenomena that need to beanalysed Presently, the study and simulation of transients in actual power systems is carried out withthe aid of a computer

Aspects that contribute to this complexity are the variety of causes, the nature of the physical nomena and the timescale of the power system transients

phe-Disturbances can be external (lightning strikes) or internal (faults, switching operations, load tions)

varia-Power system transients can be electromagnetic, when it is necessary to analyse the interactionbetween the (electric) energy stored in capacitors and the (magnetic) energy stored in inductors, orelectromechanical, when the analysis involves the interaction between the electric energy stored incircuit elements and the mechanical energy stored in rotating machines

Physical phenomena associated with transients make it necessary to examine the power system over

a time interval as short as a few nanoseconds or as long as several minutes

This latter aspect is a challenge for the analysis and simulation of power system transients, since thebehaviour of power equipment is very dependent on the transient phenomena: it depends on the range

of frequencies associated to transients An accurate mathematical representation of any power deviceover the whole frequency range of transients is very difficult, and for most components is not practicallypossible

Despite the powerful numerical techniques, simulation tools and graphical user interfaces currentlyavailable, those involved in electromagnetic transients studies, sooner or later, face the limitations ofmodels available in transients packages, the lack of reliable data and conversion procedures for parameterestimation or insufficient studies for validating models

Figure 1.1 presents a typical procedure when simulating electromagnetic transients in power systems.The entire procedure implies four steps, that are summarized as follows:

1 The selection of the study zone and the most adequate representation of each component involved inthe transient

The system zone is selected, taking into account the frequency range of the transients to besimulated: the higher the frequencies, the smaller the zone modelled In general, it is advisable tominimize the study zone, because a larger number of components does not necessarily increase

Figure 1.1 Simulation of electromagnetic transients in power systems.

accuracy; instead it will increase the simulation time, and there will be a higher probability ofinsufficient or incorrect modelling Although many works have been dedicated to providing guidelines

on these aspects [1–3], some expertise is usually needed to choose the study zone and the models

2 The estimation of parameters to be specified in the mathematical models

Once the mathematical model has been selected, it is necessary to collect the information that could

be useful for obtaining the values of parameters to be specified For some components, these valuescan be derived from the geometry; for other components these values are not readily available andthey must be deduced by testing the component in the laboratory or carrying out field measurements

In such case, a data conversion procedure will be required to derive the final parameter values Details

of parameter determination for some power components were presented in [4]

Interestingly, an idealized/simplified representation of some components may be considered whenthe system to be simulated is too complex This representation will enable the data file to be editedand the analysis of the simulation results to be simplified

A sensitivity study should be carried out if one or several parameters cannot be accurately mined Results derived from such a study will show what parameters are of concern

deter-3 The application of a simulation tool

The steadily increasing capabilities of hardware and software tools have led to the development ofpowerful simulation tools that can cope with large and complex power systems Modern software for

transient analysis incorporates powerful and friendly graphical user interfaces that can be very usefulwhen creating the input file of the test system model.

4 The analysis of simulation results

Simulation of electromagnetic transients can be used, among other things, for determining ponent ratings (e.g insulation levels or energy absorption capabilities), testing control and protectionsystems, validating power component representations or understanding equipment failures A deepanalysis of simulation results is an important aspect of the entire procedure, since each of these studiesmay involve an iterative procedure in which models and parameters values must be adjusted

com-Pioneering work in this field was presented in [2, 5, 6]; see also [7] Readers interested in netic transient analysis can consult other specialized literature [8–15]

electromag-1.2 Scope of the Book

This book provides a basic background to the main solution techniques presently applied to the calculation

of electromagnetic transients, gives details of the main applications of the most popular transient tools(insulation coordination, power electronics applications, protection) and discusses new developments(e.g dynamic average models, interfacing techniques) mostly aimed at overcoming some limitations ofthe present software tools

The main topics to be covered by this book are as follows:

Solution Methods and Simulation Tools: The analysis of electromagnetic transients in power systemscan be performed in either the time or the frequency domain Although time-domain solution meth-ods are the most common option, frequency-domain analysis offers certain features that complementthe advantages of time-domain analysis [16–18] In addition, the calculation of the steady state of apower system, prior to the calculation of a transient process, is usually performed in the frequencydomain

Tools for electromagnetic transient simulation are classified into two main categories [19]: off-lineand real-time The purpose of an off-line simulation tool is to conduct simulations on a generic computer.Off-line tools are designed to use numerical methods and programming techniques without any time con-straint and can be made as precise as possible within the available data, models and related mathematics.Real-time (on-line) simulation tools are capable of generating results in synchronism with a real-timeclock, and have the advantage of being capable of interfacing with physical devices and of maintain-ing data exchanges within the real-time clock [20, 21] Computations in real time, imposes importantrestrictions on the design of such tools, but they can be extremely useful for testing and designing powerequipment

The chapters dedicated to these topics detail currently applied methods for steady-state and transientsolution of power systems and control systems, they provide an overview of simulation tools andmethods for the computation of electromagnetic transients, including practical examples, and theydiscuss limitations

Although parallel computation is covered in the chapters related to real-time simulation, readersinterested in the computation of electromagnetic transients using a multicore environment are advised toconsult reference [22]

Modelling and Parameter Determination: Despite the powerful numerical techniques, simulation toolsand graphical user interfaces currently available, a lack of reliable data, standard tests and conversionprocedures generally makes the determination of parameters one of the most challenging aspects ofcreating a model [4] Although there is no specific chapter of this book dedicated to these topics, manyissues connected to modelling guidelines are presented in several chapters, and two annexes covering

aspects related to the development of models and calculation of parameters for electromagnetic transientsstudies have been included:

rFitting Techniques: When parameter determination is based on a frequency response test, a data

conversion procedure is usually required, in which a fitting procedure is always needed Althoughsimilar fitting techniques can be used for all power components whose behaviour can be derivedfrom a frequency response test, the optimal procedure to be applied in each case is different Annex

A presents the application of fitting techniques for extracting rational models of lines, cables andtransformers from frequency response tests [23]

rDynamic System Equivalents: A common practice when dealing with large power systems in transient

studies is to divide the system into a study zone, where transient phenomena occur, and an externalsystem encompassing the rest of the system The study zone is represented in detail, while the rest

of the system is modelled by an equivalent Given the frequency range with which transients aregenerated, there is a need for suitable techniques that could accurately determine the parameters ofthe external equivalent system from low- to high-frequency behaviours Annex B reviews currenttechniques for obtaining dynamic system equivalents [24]

Readers interested in modelling guidelines and parameter determination for electromagnetic transientsstudies can consult references [1–7]

Overvoltage Calculations: An overvoltage is a voltage having a crest value exceeding the correspondingcrest of the maximum system voltage Overvoltages can occur with very wide range of waveshapes anddurations Types and shapes of overvoltages, as well as their causes, are well known; they are classified instandards (IEC, IEEE) The magnitude of external lightning overvoltages remains essentially independent

of the system design, whereas that of internal switching overvoltages increases with the operatingvoltage of the system The estimation of overvoltages is fundamental to the insulation design of powercomponents, and to the selection of protection devices [25, 26] Chapter 5 summarizes the differenttypes of overvoltages and their causes, provides modelling guidelines for digital simulation using atime-domain tool (e.g an EMTP-like tool) and presents some illustrative cases of any type of voltagestress in power systems

Power Electronics Applications: Power electronics applications have quickly spread to all voltagelevels, from extra high voltage (EHV) transmission to low voltage circuits in end-user facilities Theyinclude high-voltage DC (HVDC) systems [27], flexible AC transmission systems (FACTS) [28], custompower devices [29], high-power AC to DC converters, converter-based drive technologies, instantaneousbackup power systems and power-electronic interfaces for integration of distributed energy resources(DER) [30] Power electronics modelling and simulation are especially important for a concept validationand design iteration during new product development Four chapters of this book have been dedicated

to the simulation of power electronics components They provide general modelling guidelines andprocedures for simulation of the main power electronics applications using a time-domain tool (e.g anEMTP-like tool), and present several case studies

Dynamic Average Modelling: Detailed switching models of power electronics converters are tionally intensive and can be the bottleneck for system-level studies with a large number of componentsand controllers These drawbacks have led to the development of the so-called dynamic average-valuemodels (AVM) in which the effect of fast switching is neglected or averaged within a prototypical switch-ing interval [31] The resulting models are computationally efficient and can run orders of magnitudesfaster than the original models Chapter 10 describes methods of constructing AVMs and demonstratestheir advantages with some practical examples

computa-Protection Systems: Protection systems are critical power system components and their behaviour is animportant part of power system response to a transient event A system aimed at protecting against over-currents consists of three major parts: instrument transformers (current, wound electromagnetic voltage,and coupling capacitor voltage transformers), protective relays, and circuit breakers [32–34] Chap-ter 11 summarizes models for instrument transformers and different types of relays (electromechanical,static/electronic, microprocessor-based), and presents some illustrative cases of protection systems.

Smart Grids: The smart grid may be seen as an upgrade of the current power system, in whichpresent and new functionalities will monitor, protect and automatically optimize the operation of itsinterconnected elements to maintain a reliable and secure environment The smart grid will offer bettermanagement of energy consumption by the use of advanced two-way metering infrastructure and real-time communication; improved power reliability and quality; enhanced security by reducing outages andcascading problems; and better integration of DERs Although the smart grid will build upon the basicdesign of the current power grid, it will have features essential to its operation that will involve monitors,sensors, switching devices and sophisticated two-way communication systems that will allow it to be ahighly automated power delivery system [35, 36]

The complete model of an actual smart grid should include the representation of: (1) conventionalpower components that will generate and transmit the electric energy, (2) various types of power-electronic interfaces, loads and DERs, plus their corresponding controllers, and (3) the two-way com-munication system To date, there is no software tool capable of coping with such a complex model,although some work is in progress [37]

Chapter 12 presents the application of time-domain solution techniques to the study of large actualdistribution systems The chapter covers the study of DER integration and its possible effects on systemreliability and voltage violations, the application of system reconfigurations by large numbers of switchingoperations to exploit the advantage of automation and self-healing capabilities and the analysis ofdistribution system overvoltages The chapter also describes some experiences with the development

of industrial-grade translators for interfacing Power-Flow programs with EMTP-like tools, which canfacilitate the simulation of electromagnetic transients to utilities

Interfacing Techniques: Interfacing an electromagnetic transient tool with external programs or rithms expands their applicability to areas where techniques are available through the external agent(program or algorithm) [38–40] Chapter 13 describes methods for interfacing a transient simulation toolwith other mathematical algorithms to extend their application for both analysis and design of complexpower systems

[8] Dommel, H.W (1986) ElectroMagnetic Transients Program Reference Manual (EMTP Theory Book),

Bonneville Power Administration, Portland, OR, USA.

[9] Greenwood, A (1991) Electrical Transients in Power Systems, 2nd edn, John Wiley & Sons, Inc., New York,

NY, USA.

[10] van der Sluis, L (2001) Transients in Power Systems, John Wiley & Sons, Ltd, Chichester, UK.

[11] Chowdhuri, P (2003) Electromagnetic Transients in Power Systems, 2nd edn, RS Press-John Wiley & Sons,

Ltd, Taunton, UK.

[12] Watson, N and Arrillaga, J (2003) Power Systems Electromagnetic Transients Simulation, The Institution of

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[13] Shenkman, A.L (2005) Transient Analysis of Electric Power Circuits Handbook, Springer, Dordrecht, The

Netherlands.

[14] Das, J.C (2010) Transients in Electrical Systems Analysis, Recognition, and Mitigation, McGraw-Hill, New

York, NY, USA.

[15] Ametani, A., Nagaoka, N., Baba, Y and Ohno, T (2013) Power System Transients: Theory and Applications,

CRC Press, Boca Raton, FL, USA.

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[18] Moreno, P and Ramirez, A (2008) Implementation of the Numerical Laplace Transform: A review IEEE

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power systems: Overview and challenges IEEE Transactions on Power Delivery, 24(3), 1657–1669.

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The computation of a power system load-flow falls into the steady-state category It is often based onthe positive sequence approximation of the studied network The positive sequence approximation usesthe balanced network assumption: balanced loads and continuously transposed transmission lines It isoften an acceptable approximation for balanced transmission systems, but in some systems transmissionlines may not be balanced, and unbalanced loading may occur Distribution systems are not balanced bynature and require multiphase and unbalanced load-flow calculation methods The load-flow solution isthe first initialization stage of a power system It determines all the voltage phasors in the studied systemand establishes all the initial conditions.

The load-flow solution of a power system is a nonlinear problem that can be solved using Jacobianmatrices and iterations When all the load-flow constraints are converted into lumped branch equivalentmodels, it is possible to achieve a linear steady-state solution without iterations

Electromechanical transients assume low-frequency perturbations and are conventionally solved usingthe positive sequence network approximation The power system is assumed to remain in quasi steady-state, whereas the generating units (synchronous or asynchronous machines) are solved using differentialequations in the time-domain Such methods can be efficiently used to simulate and study very-large-scale systems for rotor angle stability problems, including large disturbances and small-signal stabilityproblems

Transient Analysis of Power Systems: Solution Techniques, Tools and Applications, First Edition.

Edited by Juan A Martinez-Velasco.

© 2015 John Wiley & Sons, Ltd Published 2015 by John Wiley & Sons, Ltd.

The category of electromagnetic transients avoids approximations and becomes applicable to thewidest range of frequencies Studied phenomenon signals are visualized in the time-domain at thewaveform level and can contain frequencies from 0 Hz to 100 kHz or higher Using such a wideband offrequencies requires detailed circuit-based calculation methods and models The modelling sophistication

is linked to the frequency content Electromagnetic transients include electromechanical transients andrequire load-flow solution for initialization Due to the detailed representation of circuit components andincreased precision, the computation of electromagnetic transients requires more computing resourcesand consequently significantly more computing time

Software packages and methods used for computing electromagnetic transients are called netic transient-type (EMT) tools EMT-type simulation methods are classified into two main categories:off-line and real-time The purpose of an off-line simulation tool is to conduct simulations on a genericcomputer Off-line tools are designed for high efficiency using powerful graphical user interfaces, numer-ical methods and programming techniques Such tools do not have any computing time constraints andcan be made as precise as needed within the available data, models and related mathematics

electromag-Real-time simulation tools are capable of generating results in synchronism with a real-time clock.Such tools are capable of interfacing with physical devices and maintaining data exchanges within thereal-time clock The capability to compute and interface in real time, imposes restrictions on the design

of such tools Computing technologies and numerical methods are, however, evolving rapidly, and thegap between real-time and off-line methods is constantly reducing

This chapter targets mainly off-line solution methods and tools The objective is to provide an overview

of off-line simulation tools and methods for the computation and analysis of electromagnetic transients.This chapter focuses on the most widely recognized and available groups of methods applied in industrialgrade computer software packages

This chapter follows the initial work presented in [1–4]

2.2 Application Field for the Computation of

Electromagnetic Transients

The initial application of EMT-type tools was the computation of overvoltages in power systems Thereare four main categories of overvoltages: very fast front, fast front, slow front and temporary The veryfast front category is related mainly to restrikes in gas-insulated substations The frequencies range from

100 kHz to 50 MHz Lightning overvoltages fall into the fast front category, their typical frequencycontent being from 10 kHz to 3 MHz Switching overvoltages fall into the slow front category withfrequencies ranging from fundamental frequency to 20 kHz Switching events are internal controlled

or uncontrolled events For example, controlled events are line switching actions Faults on buses or

in transmission lines fall into the list of uncontrolled events For temporary overvoltages, the typicalcauses are: single-line-to-ground faults causing overvoltages on live phases, open line energization andload-shedding In some cases, temporary overvoltages are combined with ferroresonance The frequencycontent for temporary overvoltages is typically from 0.1 Hz to 1 kHz

Frequencies above the fundamental frequency usually involve electromagnetic phenomena cies below the fundamental frequency may also include electromechanical modes (synchronous orasynchronous machines)

Frequen-The above categories can be expanded to list specific important study topics in power systems:

rdetailed behaviour of synchronous machines and related controls, auto-excitation, subsynchronousresonance, power oscillations

These applications are in a wideband range of frequencies, from DC to 50 MHz EMT-type methods arealso applicable to the simulation and analysis of electromechanical transients EMT-type programs canproduce more precise simulation results for such studies due to inherent modelling capabilities to accountfor network nonlinearities and unbalanced conditions Frequency-dependent and voltage-dependent loadmodels can also be incorporated in EMT-type tools

Since EMT-type programs are able to represent the actual circuit of a power network, they are moregeneral than traditional power system analysis tools EMT-type methods constitute the precision referencefor power system analysis

The main modules of an EMT-type simulation tool are:

1 graphical user interface (GUI)

2 load-flow solution

3 steady-state solution

4 initialization: automatic or manual initial conditions

5 time-domain solution

6 waveforms and outputs

These modules are described in the following sections The steady-state solution is based on lumpedcomponent models with parameters derived from the load-flow solution phasors As shown below, theload-flow solution is based on constraints at various buses and requires a nonlinear system solver

In addition to the above fundamental modules, EMT-type tools may include an external interface foruser-defined models and communication with other solution methods or complete software packages.Statistical analysis modules can be included to generate, for example, random switching timings forestimating the worst overvoltage conditions A set of defined parameters may be perturbed using specificrules or random numbers, to perform parametric studies where the simulations are executed for each set

of parameters to present an ensemble of results submitted to various analysis options and optimizations[5, 6]

2.4 Graphical User Interface

The graphical user interface is the first entry level to the simulation process It is the simulated networkdata input method Modern applications rely on GUIs for preparing data and controlling the simulationprocess GUIs with various levels of flexibility and visualization capabilities allow us to draw the circuitdiagram of the simulated system and enter all the appropriate data for selected models In most cases theGUI is just used to generate a data file that is submitted directly to the computational engine The GUImay also maintain a permanent and dynamic link with the computational engine for exchanging data,visualization of intermediate results and manipulating parameters

An example of a GUI-based design is shown in Figure 2.1 Modern GUIs are based on the hierarchicaldesign approach with subnetworks and masking Subnetworks allow us to simplify the drawing and hidedetails while masking provides data encapsulation The design of Figure 2.1 uses several subnetworks.The 230 kV network is interconnected with a 500 kV network evacuated with all its details into thesubnetwork shown in Figure 2.1 In a hierarchical design subnetworks can also contain other subnetworks.Subnetworks can be also used to develop models The three-phase transformers shown in Figure 2.1 are

Figure 2.1 Sample 230 kV network simulation presented in a GUI.

based on the interconnection of single-phase units The synchronous machine subnetworks contain theload-flow constraints, machine models and the subnetwork composed of voltage regulator and governorcontrol subnetworks, as shown in Figure 2.1

Although several advanced GUIs [7–9] are currently available, the industry lacks interoperabilitystandards between various software applications Currently there are no applicable standards for transient(EMT-type) model data fields This means that the GUIs and related data files are based on proprietaryformats that cannot be decoded by other applications This situation creates major bottlenecks whendifferent software tools are used within a given organization or when different applications are used

in one or more collaborating organizations Some applications provide external access functions andmight be called directly from other applications for performing simulations on assembled networks Theprogramming aspects of such applications are not complex, but interfacing networks solved in differentcomputational engines may become error prone or create numerical instabilities due to inherent lack ofsimultaneous solution capability

A possible solution to data portability between applications is the utilization of the common mation model [10] (CIM) format in the simulation of electromagnetic transients The CIM format is anopen standard for representing power system components It could be used for electromagnetic transients

infor-if augmented with the needed data fields related to such models An experiment with CIM/XML datatranslation into a proprietary format and GUI drawing is presented in [11]

Standardization of data is also an important part of the solution for creating portability with otherconventional power system applications Standardization should result in significant benefits to the powerindustry

2.5 Formulation of Network Equations for Steady-State

and Time-Domain Solutions

EMT-type programs are based on the representation of the actual electrical circuit equivalent of thestudied power system The most common network equation formulation methods fall into two maincategories: nodal analysis and state-space

Bold characters are used hereafter for the representation of vectors and matrices

2.5.1 Nodal Analysis and Modified-Augmented-Nodal-Analysis

used for computing the sum of currents entering each electrical node

node It is assumed that the network has a ground node at zero voltage which is not included in equation(2.1) Since the network may contain voltage sources (known node voltages), equation (2.1) must bepartitioned to keep only the unknown voltages on the left-hand side:

v′

n v s]T

individual device (network component) admittance matrices at each node A given device (network

component) connected between left node k and right node m, is described through its generic admittance

accommodate any number of phases and coupling between phases If the device model includes current

n) in (2.1)

Equation (2.1) has several limitations It is restricted to modelling devices with the admittance matrixrepresentation of (2.3) and ideal voltage sources connected to ground It is not possible, for example, todirectly model branch relations such as ideal transformer units or ideal sources without a ground node.Ideal transformer units are used as primitive devices for building three-phase transformer models It is

current relations cannot be represented directly

The above limitations can be eliminated using modified-augmented-nodal analysis (MANA) duced in [12] for an EMT-type solution method and improved in [13, 14] Equation (2.1) is augmented

intro-to include generic device equations, and the complete system of network equations can be rewritten inthe more generic form:

currents in device models; v x is the vector of known voltages; x N=[

v n i x]T

i n v x]T

Inreality the network component equations can be entered in any order in equation (2.4) and other types ofunknown/known variables can be used, but the partitioning presented in (2.5) allows us to simplify theexplanations Further details can be found in [13, 14]

As will be shown below, (2.4) (or (2.5)) can be used for both steady-state and time-domain solutions

of a generic network and allows us to integrate generic model equations such as

can also include coupling by rewriting it with vectors and matrices A three-phase voltage source, for

example, connected between two arbitrary nodes k and m is expressed as

Equation (2.7) can be rewritten in its single-phase form using scalars

For a single-phase switch model there are two states In the closed state

is appearing in series with the switch It is noticed that changes in switch status in the time-domain

Single-phase and three-phase transformers can be built using the ideal transformer unit representationshown in Figure 2.2 It consists of dependent voltage and current sources The secondary branch equation

is given by

Figure 2.2 Ideal transformer model

where g is the transformation ratio This equation contributes its own row to the matrix Ar, whereas

a similar manner, with a complex g in the steady-state formulation It is possible to extend to multiple

secondary windings using parallel-connected current sources on the primary side and series-connectedvoltage sources on the secondary side Leakage losses and the magnetization branch are added externally

to the ideal transformer nodes

Three-legged core-form transformer models – or any other types – can be included, using coupledleakage matrices and magnetization branches

The MANA formulation (2.4) is completely generic and can easily accommodate the juxtaposition

of arbitrary component models in arbitrary network topologies with any number of wires and nodes It

is not limited to the usage of the unknown variables presented in (2.5) and can be augmented to usedifferent types of unknown and known variables It is conceptually simple to realize

2.5.1.1 Steady-State Solution

The steady-state version of equation (2.4) is based on complex numbers Equation (2.4) is simplyrewritten using capital letters to represent complex numbers (phasors) If a network contains sources atdifferent frequencies, then (2.4) can be solved at each frequency and assuming that the network is linear

steady-state solution in the form of a Fourier series

The time-domain module is the heart of an EMT-type program It starts from 0-state (all devices areinitially de-energized) or from given automatic or manual initial conditions and computes all variables

as a function of time using a time-step Δt.

Since component models may have differential equations, we need to select and apply a numericalintegration technique for their solution Since many electrical circuits result in a stiff system of equations,the chosen numerical integration method must be stiffly stable Such a need excludes explicit methods

In the list of implicit numerical integration methods, the most popular method in industrial applicationsremains the trapezoidal integration method It is an A-stable polynomial method that can be programmedvery efficiently If an ordinary differential equation is written as

dx

dt = f (x, t) x(0) = x0,

The terms found at t − Δt constitute history terms, and all quantities at time-point t are also related

through network equations The computation process finds a solution at discrete time-points, as illustrated

Figure 2.3 Discrete solution time-points.

device equations using a numerical integration technique such as equation (2.11) For a pure inductor

branch connected between two nodes k and m

where the km subscript is dropped to simplify the notation Since the last two terms of this equation

represent computations available from a previous time-point, it can be written as

i t = Δt

An equation similar to (2.14) can be written for capacitor branches The inductor, capacitor and resistorare primitive elements for building other models All discretized device equations are entered into (2.4)which must be written as

A N

tx N

t = b N

for the solution at the time-point t.

the network contains transmission lines or cables The models of such devices have a propagation delaywhich creates a natural decoupling of the studied network into subnetworks that can be solved in parallel.The companion branch approach is used in several EMT-type tools [13, 16–18]

2.5.1.3 Nonlinear Devices

An important problem in the time-domain computation of power system transients is the solution ofnonlinearities Such nonlinearities occur due to nonlinear functions being used in some network device

Figure 2.4 Sample nonlinear symmetric function.

models In most cases, a nonlinear function can be modelled using piecewise linear segments Thepositive part of a sample nonlinear function with three segments is shown in Figure 2.4 for a voltage

is assumed that there is a unique solution for a given voltage Each segment j can be represented by a

operation point for the voltage solution at the time-point t.

Equation (2.16) can be also written in its vector-matrix form for coupled nonlinearities

In some cases, the piecewise linear representation is not realizable beforehand In such cases, thelinearization equation (2.16) must be recalculated at each network solution time-point A typical example

is the breaker arc model, the nonlinear function based arrester model or the case of a generic black-boxdevice

There are two main categories of methods for solving nonlinear functions: with and without solutiondelays The delay is a numerical integration time-step delay In some methods the nonlinear model

is represented through a voltage-dependent current source Such methods may encounter numericalinstabilities More robust methods rely on linearization at the operating point As explained above, thelinearization results in an equivalent Norton circuit Norton equivalents can also be used for interfacingwith more complex nonlinear devices and rotating machine models [19]

In delay-based methods the Norton equivalent is updated with a time-step delay The delay-basedmethods are also called pseudo-nonlinear methods [20], whereas methods without delays are calledtrue-nonlinear methods

If there is no artificial delay, then in a coupled subnetwork all nonlinear devices must be solvedsimultaneously A coupled subnetwork is defined here as a physical subnetwork in which all devices arerelated to each other at a given solution time-point and there are no delay elements, such as distributedparameter transmission lines or cables Such a subnetwork actually creates an independent set of equations

or matrix blocks in equation (2.5) The simultaneous solution means that if at a given solution time-pointthe node voltage of a device modifies its current (or equivalent model) then it is necessary to update andresolve the subnetwork nodal equations until all voltages stop changing within a given tolerance Theconvergence of voltages must occur before moving to the next solution time-point

In delay-based methods the device equations (or currents) are updated without recalculating theirvoltages at the same time-point and through the coupled subnetwork The solution is advanced to thenext time-point without recalculating the voltages in the subnetwork If the time-step is sufficiently small,

Figure 2.5 Two networks separated using the compensation method.

this method can become sufficiently precise, but in some cases it may still create numerical problems orforce abnormally small time-steps

Simultaneous solution methods are more precise and are almost unavoidable in most cases

2.5.1.3.1 Compensation Method

A powerful and efficient method applied in some programs is the compensation method For historicalreasons this method is poorly understood in the literature, and its limitations are not well known It isalso often reused or reinvented without recognizing or referring to the original idea

The compensation method was originally introduced in [21, 22] and applied to EMT-type simulations

in [20] The basic idea is the separation of a network into two parts, as shown in Figure 2.5, networksN1 and N2 This separation can be also used in independent subnetworks As explained above, thesesubnetworks are created naturally due to propagation delay decoupling of transmission line or cablemodels

If the network N1 is a linear network, then N2 can be the compensation-based network The networkN2 can have the following properties:

The basic principle is the computation of a Thevenin equivalent for the network N1 The following

steps are applied in the compensation process at a given solution time-point t:

1 The network N1 is solved first without N2 (N2 is disconnected) This results in the computation ofall node voltages in N1

2 The Thevenin equivalent of N1 is established from the voltage computations in the previous step and

3 The network N2 is solved with the Thevenin equivalent of N1

4 All active sources in N1 are killed, and the currents entering N2 are used to find all network voltages

N1 due to its internal sources only (N2 is disconnected), then the compensated solution becomes (at agiven time-point)